(a) Calculate the activity of one mg sample `._(28^(Sr^(90)))` whose half life period is `28` years.
(b) An experiment is performed to determine the half-life of a radioactive substance which emits one beta particle for each decay process. Observation shown that an average of `8.4 beta-`particles are emitted each second by `2.5 mg` of the substance. the atomic weight of the substance is `230`. calculate the half0life of the substance.
(c) Determine the quantity of `._(84^(Po^(210)))` necessary to provide a source of alpha particle of `5mCi` strength (`T_(1//2)` for Po `= 138` day).

Explanation

(a) Number of atoms
`N = (mass)/(At.wt.) xx N_(A)`
`= (1xx10^(-3))/(90) xx 6.023 xx 10^(23)`
`= 6.7 xx 10^(18)`
`lambda = (ln2)/(T_(1//2)) = (0.693)/(28)//year`
`A = lambdaN = (0.693)/(28) xx 6.7 xx 10^(18) = 0.16 xx 10^(18)//year`
`= (0.16 xx 10^(18))/(365xx24xx3600) = 5xx10^(9) dps`
(b) `N = (2.5xx10^(-3))/(230)xx6.023 xx 10^(23) = 6.5 xx 10^(18)`
`A = 8.4//sec`
`=lambdaN = (ln2)/(T_(1//2))N rArr T_(1//2) = (ln2)/(A)N`
`T_(1//2) = (0.693xx6.5 xx 10^(18))/(8.4) = 0.54 xx 10^(18) sec`
`= 1.7 xx 10^(10) year`
(c ) `A = lambdaN`
`N = (A)/(lambda)`
`(m)/(m) xx N_(A) = (A)/(lambda) = (A)/(In2//T_(1//2))`
`m = (AMT)/((ln2)N_(A))`
`= (5xx10^(-3)xx3.7 xx 10^(10)xx210xx138xx24xx3600)/((0.693)(6.023 xx 10^(23)))`
`1.1 xx 10^(-3)g = 1.1mg`